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The Economic Benefits of Computer-Integrated Manufacturing (Paper I)
Ayres, R.U. & Funk, J.L.
IIASA Working Paper
WP-87-039
May 1987
Ayres RU & Funk JL (1987). The Economic Benefits of ComputerIntegrated Manufacturing (Paper I). IIASA Working Paper. IIASA, Laxenburg, Austria: WP87039 Copyright © 1987 by the author(s). http://pure.iiasa.ac.at/id/eprint/3013/
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Working Paper
THE ECONOMIC BENEFITS OF COMPUTER-INTEGRATED MANUFACTURING (PAPER I)
Robert U. Ayres, IIASA
Jeffrey L. Funk, Westinghouse Electric Corporation
May 1987
WP-87-39
International Institute for Applied Systems Analysis A-2361 Laxenburg, Austria
NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR
THE ECONOMIC BENEFITS OF COMPUTER-INTEGRATED MANUFACTURING (PAPER I)
Robert U. Ayres, IIASA
Jeffrey L. Funk, Westinghouse Electric Corporation
May 1987
W-87-39
Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily repre- sent those of the Institute or of its National Member Organizations.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 Laxenburg, Austria
FOR EVORD
Two pape r s a r e p re sen ted h e r e t o g e t h e r i n one package. The
f i r s t which f o l l o w s , is a g e n e r a l i n t r o d u c t o r y and t h e o r e t i c a l
d i=cuss ion of t h e problem of economic b e n e f i t s e s t i m a t i o n f o r CIM
t e c h n o l o g i e s . I t was w r i t t e n by Robert U . Ayres, l e a d e r of t h e
CIM p r o j e c t and J e f f r e y L. Funk, now a t Westinghouse R&D c e n t e r .
The second paper p r e s e n t s a p a r t i c u l a r (macroeconometric>
methodology a s a p p l i e d t o t h e b e n e f i t s of r o b o t s and NC machine
t o o l s f o r a s i n g l e count ry : Japan. I t was w r i t t e n by Shunsuke
Mori, a member of t h e CIM p r o j e c t team a t IIASA. I t is hoped
t h a t t h e r e s u l t s w i l l be of c o n s i d e r a b l e i n t e r e s t i n themse lves ,
a s wel l a s p rov id ing a v i a b l e model f o r f u t u r e e x t e n s i o n t o o t h e r
c o u n t r i e s .
Two e a r l i e r CIM Working Papers a r e r e l e v a n t t o t h e
approaches d i s c u s s e d h e r e , namely C Ayres 86f I and C Ayres 87bl .
Thomas H . Lee Program Leader Technology, Economy, S o c i e t y
The Economic Benef it of Computer- Inte~rated Manuf acturinqr
Introduct ion2,
The evolution of manufacturing technology from the
1820's until after World War I 1 can be characterized broadly
as exploiting economies of mechanization, specialization,
standardization, and scale. On an aggregate level, the
productivity of workers was enormously increased by
mechanization, subdividing, and rationalizing complex non-
repetltlve tasks into a sequence of simpler repetitive ones,
higher precision, and higher operating rates of machine
tools, mass production of truly interchangeable standard
parts, use of dedicated automatic machines to maximize parts
output rates, and mechanical assistance for parts handling
and assembly. Labor productivity improvements from the
1828's to the 1958's vary from one product to another, but in
many cases the overall improvement was several orders of
magnitude. Metal cutting rates, for example, increased by
over 18@ times from 1898 to 1978. However, by 1978 the
potential for further improvements along the same lines was
far more modest in most cases. Since 1958, the emphasis has
shifted toward programmability and flexibility. The driving
force for this shift arises out of the growing complexity and
'Computer Integrated Manufacturing (CIM) refers to the use of computers to control the manufacture of discrete items. It covers, therefore, materials handling and storage, cutting, forming and shaping, parts, heat treating, surface finishing, j oining Ce. g. welding), assembly, and inspect ion. It also covers associated "overhead" activities such as design, product ion, engineering, quality control, plant operation, and internal maintenance, and packing and shipping.
"This section has been taken from the prospectus for the CIM project C I IASA, September 30, 1986).
- 2 -
d i v e r s i t y of t h e modern i n d u s t r i a l economy.
I n c r e a s i n g l y , t h e problem of p r o d u c t i o n is a problem of
r e s o u r c e p l a n n i n g (1.e . c o o r d i n a t i n g s u p p l i e r s and o p t i m i z i n g
m a t e r i a l s h a n d l i n g ) and of i n v e n t o r y management. From
a n o t h e r p e r s p e c t i v e , t h e problem of manufac tu r ing is
i n h e r e n t l y i n f ormat i o n - i n t e n s i v e , i n v o l v i n g many t e n s of
t h o u s a n d s of b i n a r y go/no ( y e s / n o > d e c i s i o n s based on s e n s o r y
d a t a g a t h e r e d a t many p o i n t s i n s p a c e and t i m e abou t t h e
s t a t e of e a c h t o o l , e a c h component, e a c h subsys tem, and t h e
p roduc t i o n env i ronment . H i s t o r i c a l l y , o n l y human workers
have had t h e s e n s o r y c a p a b i l i t y t o a c q u i r e and i n t e r p r e t t h e
d a t a needed t o make t h e s e b i n a r y go/no d e c i s i o n s . However,
s i n c e t h e e a r l y 1 9 8 0 ' s manufac tu r ing f i r m s have begun t o have
a n a v a i l a b l e a l t e r n a t i v e t o humans: t h e machine o r r o b o t
c o n t r o l l e d by a " smar t s e n s o r " .
The a c c u m u l a t i o n of t e c h n o l o g i c a l changes i n s o l i d - s t a t e
e l e c t r o n i c s and computer s c i e n c e s i n c e t h e mid-28th c e n t u r y
seems t o have f i n a l l y r e a c h e d a c r i t i c a i p o i n t . S o l i d - s t a t e
m i c r o p r o c e s s o r s l i n k e d t o s o l i d - s t a t e s e n s o r y d e v i c e s w i l i
soon b e g i n t o o f f e r more a c c u r a t e and r e l i a b l e means of
c o o r d i n a t i n g t h e complex p r o c e s s e s r e q u i r e d i n modern
manufac tu r ing . "Smart s e n s o r s " a r e c r i t i c a l b u i l d i n g b l o c k s
of t h e f o r e s e e a b l e computer- i n t e g r a t e d , unmanned
manufac tu r ing p l a n t of t h e f u t u r e . "
I t is one p r imary h y p o t h e s i s of t h e CIM s t u d y t h a t t h e
d r i v i n g f o r c e beh ind t h i s change is no t a wish t o a v o i d h i g h
. ..,
.:-.For a more e x t e n d e d d i s c u s s i o n of t h e s e i s s u e s i n t h e CIM Working Paper s e r i e s s e e [ A y r e s 8 6 f , Ayres 8 7 b l .
"See Ayres I: Ayres & Funk 8 5 , Ayres 8 6 ~ 1 , a r t i c l e s fo r thcoming i n R o b o t i c s J o u r n a l and Prometeus .
- 3 - labor costs per se, but the need to escape from the
bureaucratic inflexibility of organizations and the physical
inflexiblity of mechanisms that were the price of relying on
error-prone human workers for all of the micro-scale
information processing functions in the conventional factory.
Ultimately, it may be the desire to continually increase
reliability and quality without sacrificin~ flexiblity that
is the chief driving force behind the trend toward computer
integrated manufacturing.
In addition, we hope to test several subsidiary*
hypotheses:
- that flexiblity to respond quickly to market changes is
at best a secondary motivation for most early users in
the first tier (systems integrators) and third tier
suppliers (job shops), but may become a strong
motivation for second-tier suppliers currently dependent
on "Detroit Automation".
- that, currently, CIM is not needed by large-scale
producers (systems integrators) to achieve maj or
inventory savings and faster turnaround, and that CIM
will get increased attention by these manufacturers only
after the "easy" savings from statistical quality
control, ' just-in-time' methods (kan-ban) , or materials-
resource planning (MRP) have already been achieved. CIM
may offer more immediate benefits to second tier
suppliers who are under increasing pressure from their
customers to meet more exacting delivery schedules, with
shorter production runs.
- that economies of scale will have a decreasing influence
in coming decades, whereas economies of scope (1. e.
capital sharing facilitated by increased flexibility)
will have an increasing influence.
- that, as a consequence of increasing flexiblity of major
second-tier suppliers, the traditional niche for
specialty subcontractors and suppliers will erode.
Benefits Measurement
The various hypotheses stated above imply that improved
product quality and increased flexibility in the use of
capital are beneficial to users of CIM. However the argument
thus far is only qualitative. To carry it a step further one
must define quality and flexibility more precisely and
formulate them in terms of conventional economic variables
and models. This is the next task to be undertaken, and it
is a vital one.
To organize the discussion, it is helpful to consider
five possible kinds of economic benefit. The list follows:
1. Labor savinx. Some CIM technologies (most notably
robots) can be regarded as direct substitutes for semi-
skilled human labor. This means that robots (sometimes
called "steel collar workers") can also be regarded as
additions to the labor force, although their 'wages' are
partly operating costs and partly costs of capital.
2. Capacity augmentinq. Some CIM technologies, such as
scheduling systems and programmable controllers (PC's)
with sensory feedback, can be regarded as creating
additions to capacity. This is the case to the extent
that they increase the effective utilization of existing
machine tools and other capital equipment (e. g. by
permitting unmanned operat ion at night > or permit faster
turnarounds and reductions in the inventory of work-in-
progress. The productivity of capital is thus
increased.
3. Capital-sharing. The major benefit of "flexibility", as
the concept is normally understood, is that it permits
faster response to changing market conditions, or
superior ability to differentiate products.& The major
reason for slow response is the widespread use of
dedicated, specialized ("Detroit" > automat ion in mass
product ion. Here, the lowest possible marginal unit
cost is achieved at the expense of very high fixed
capital investment and large write-offs in case the
product becomes obsolete and cannot be sold.
Flexibility in this context is the ability to adapt (or
switch) capital equipment from one generation of a
product to the next. The term flexibility is also
widely used in a rather different context, to describe a
futuristic concept analogous to an automated job shop,
capable of producing "parts on demand". In either case,
capital is shared among several products rather than
dedicated to a single one. Evidently capital-sharing is
practically indistinguishable from capacity
augmentation. However it is perhaps slightly preferable
"A more extended discussion of the rfelationship between flexibility and product differentiability (i.e. via design change flexibility or "mix flexibility") can be found in Boyer and Cor iat (1987 > .
- 6 -
to model it as an extension of the lifetime of existing
capital or (in some cases) as credit for capital
recovery.
4. Product quality improvement. The term 'quality' is not
very precise, since it comprises at least two aspects;
(1) product reliability (defect reduction), and (2)
product performance. The latter can be disregarded,
here, as being an aspect of product change (discussed
next). It is postulated that several CIM technologies,
especially the use of "smart sensors" in conjunction
with programmable controllers, will eventually reduce
the in-process error/defect rate. Moreover, these
technologies will also permit more complete and more
accurate testing and inspection of workpieces and final
products. A quantitative measure of product
reliablility is needed, if possible, better than the
simple 'percentage of time operating' measure that
appears throughout the human factors literature C e. g .
McCormick & Sanders 821.
5. Acceleration of product performance improvement. As
noted above in connection with quality, improved product
performance can be distinguished in principle from
improved product reliability through reduced
error/defect rates. The latter is a function of the
manufacturing process only, whereas the former requires
changes in the actual design of the product. It was
pointed out that one benefit of flexiblity is that it
reduces the cost of each product change. A further
benefit is that, as a result, product redesigns are
likely to be more frequent. The problem, for an
economist, is to find empircal evidence of a
relationship between the cost of product redesign and
retooling and the rate of product performance
improvement. This appears to be a relatively unplowed
field of research, to date.
Static vs. Dynamic Approaches to Benefits Measurement
Up to this point, we have not attempted to consider the
question: benefits to whom? In fact, this is a critical
issue because short-run benefits are likely to be
appropriated mainly by producers (as profits), whereas in the
long run in a competitive economy essentially all of the
benefits will be passed on to consumers through product price
reduct ions, performance improvements, and wage increases. ".
More important for our purposes, it is only the short-
term benefits appropriable as profit by producers that can
directly motivate innovation and technological diffusion
[Mansfield 61, 681. In this context, it is clear that in a
static environment, labor saving, capacity augmentation and
capital sharing may contribute immediately to profitability.
On the other hand, product quality and performance
improvements may have a less direct impact on profitability
in the short run, except to the extent that error/defect
control has a direct effect on costs,
In a static world of competitive 'price-takers', and
given 'fixed' and 'variable' costs, the optimum (short-run
&,This effect is reflected In the long-term rise in "labor share" of output.
- 8 -
p r o f i t maximizing) p r o d u c t i o n l e v e l is d e t e r m i n e d by t h e
shape of t h e v a r i a b l e c o s t c u r v e . Assuming t h e u s u a l U-
shaped v a r i a b l e c o s t c u r v e , t h e optimum p r o d u c t i o n l e v e l is
found by e q u a t i n g marg ina l revenue and marg ina l c o s t . I f
demand i n c r e a s e s , b u t t o t a l c a p a c i t y r e m a i n s f i x e d , p r i c e s
and p r o f i t s w i l l r i se , and v i c e v e r s a . I f t h e i n d u s t r y is
p r o f i t a b l e , any e x i s t i n g ( o r new) p roducer c a n i n c r e a s e h i s
c a p a c i t y , t h u s r e d u c i n g h i s a v e r a g e c o s t s and breakeven p o i n t
and he can i n c r e a s e market s h a r e by p r i c e c u t t i n g . But i f
s e v e r a l p r o d u c e r s do t h i s , t h e r e s u l t is o v e r c a p a c i t y and
l o s s e s . Moreover, assuming n o n - c o n v e r t i b l e ( i n f l e x i b l e )
c a p i t a l , t h e e f f e c t i v e marg ina l c o s t now becomes t h e marg ina l
v a r i a b l e c o s t and e a c h c o m p e t i t o r w i l l go on p roduc ing even
i f it e a r n s no n e t r e t u r n on c a p i t a l . I n f a c t , t h e s t a t i c
c o m p e t i t i v e market is i n h e r e n t l y u n s t a b l e (and t h e r e f o r e n o t
s t a t i c ) a t any f i n i t e p r o f i t l e v e l .
In o t h e r words ( a s Schumpeter p o i n t e d o u t long a g o ) ,
p r o f i t s i n a c o m p e t i t i v e market are i n h e r e n t l y a dynamic
phenomenon r e f l e c t i n g a n e x p l o i t a b l e temporary c o s t o r p r i c e
advan tage . The advan tage a t any moment i n t i m e may be due t o
s u p e r i o r brand-name r e c o g n i t i o n , c h e a p e r l a b o r o r ene rgy
s o u r c e s , b e t t e r l o c a t i o n v i s a v i s m a r k e t s , more e f f i c i e n t
p r o d u c t i o n t e c h n o l o g y o r b e t t e r p roduc t d e s i g n . But u n l e s s
one o r more of t h e s e a d v a n t a g e s is p r o t e c t e d , e . g . by brand-
name c o p y r i g h t ( e . g . 'Coke' ) , a monopoly f r a n c h i s e (CBS) , an
i m p e n e t r a b l e s e c r e t o r a se t of i n t e r l o c k i n g p a t e n t s ,
p r o f i t a b i l i t y w i l l l a s t j u s t a s long as it t a k e s f o r a
c o m p e t i t o r t o i m i t a t e o r improve on t h e p r o d u c t and/or b u i l d
a l a r g e r o r newer p l a n t .
- 9 -
I t f o l l o w s , t h e r e f o r e , t h a t c o r ~ t i n u o u s long-term
p r o f i t a b l i t y f o r a f i r m c a n o n l y be a s s u r e d by a c o n t i n u o u s
p r o c e s s of c r e a t i n g and e x p l o i t i n g new a d v a n t a g e s (of some
k i n d ) t o r e p l a c e t h e o l d e r , d i s s i p a t i n g ones . Opening new
marke t s , a d v e r t i s i n g , p r o d u c t improvment, p r o c e s s improvement
-- a l l a r e means of c r e a t i n g c o m p e t i t i v e a d v a n t a g e s . Forward
mot i o n is e s s e n t i a l : t o be s t a t i o n a r y is t o s i n k and be
overwhelmed. A moving b i c y c l e , a l a s s o , a 'hula-hoop' , a
c h i l d ' s t o p o r a wa te r s k i a r e dynamica l ly s t a b l e ; b u t when
t h e motion s t o p s t h e s y s t e m c o l l a p s e s . The same t h i n g h o l d s
t r u e f o r s p e c i e s i n a n ecosys tem o r f i r m i n a c o m p e t i t i v e
market . There is no s a f e p l a c e t o h i d e i n d e f i n i t e l y from
hungry p r e d a t o r s s e e k i n g a meal o r hungry c o m p e t i t o r s s e e k i n g
a market .
In s h o r t , o n l y a dynamic model f i r m b e h a v i o r h a s any
v a l u e i n a s s e s s i n g t h e b e n e f i t s of CIM t e c h n o l o g i e s ( o r ,
i n d e e d , any o t h e r t e c h n o l o g i e s p rov ided e x o g e n o u s l y ) .
Fur the rmore , it is e s s e n t i a l t o view t h e f i r m i n its
c o m p e t i t i v e env i ronment . Most s i m p l e models of t h e b e h a v i o r
of t h e f i r m assume a s t a t i c envi ronment ( e . g . a r ~ exogenous
demand s c h e d u l e o r market p r i c e and n e g l e c t t h e r e a l i t i e s of
c o m p e t i t i v e r e s p o n s e . I f a l l competing f i r m s adop ted a more
e f f i c i e n t p r o d u c t i o n t e c h n o l o g y s i m u l t a n e o u s l y , none would
g a i n any s p e c i a l advan tage o v e r t h e o t h e r s b u t a l l would b e a r
t h e c o s t of t h e n e c e s s a r y inves tment . To t h e e x t e n t t h a t t h e
a d o p t i o n of more e f f i c i e n t p r o d u c t i o n p r o c e s s e s (CIM) r e s u l t s
i n lower c o s t s and t h e s e a r e s u b s e q u e n t l y p a s s e d on t o
consumers a s lower p r i c e s , t h e market f o r each p roduc t might
(or might not) grow enough to result in increased
profitability for the producer, ceteris paribus.
A Simple Dynamic Model for Estimating Private Benefits
(Profitability) of an Innovative Production Technique
Suppose, for a moment, that each CIM adopter is a
monopolist in its market 'niche' and that this market is
characterized by a constant price elasticityE'
where P is the product price and Q is the physical output <=
demand) level. The producers prof it (per unit time) can be
defined
where C is a cost function. One commonly assumed simple cost
function is the so-called 'experience curve' '<>
'At first glance this is a very heroic assumption, but it is consistent with the notion that firms with similar product ion technologies can compete by product differentiation. This formulation was introduced by Chamberlin (1933, 1953).
'""T h i assumption is also moderately heroic, though widely used in macroeconomic models. See, e. g. Houthakker & Taylor 1970.
'The experience curve is often parametrized in terms of the ratio s of end-of-period costs to beginning-of-period costs, after each doubling of cumulative output. Typical values of s range iron 8.9 to U . 6 . The lower the value of s, the faster costs are deciining. For a recent survey of the microeconomic literature relating experience curves and cost functions, see C Gul ledge and Womer 861 .
where N(t> is cumulative output up to time t
and b is a parameter characteristic of the industry (see
Figure 1). If the market demand Q is growing exponentially
at a rate K
then it follows from (1) that
and from ( 5 ) and ( 6 ) that
whence
where
i Semi-conductor active elements (1 964-1 977) $/unit
MOS dynamic RAM production (1973-78) $/kilobit Integrated circuits (1 964-72) $/unit* Free-standing gas ranges (1 947-67) $/unit
Digital watches (1975-78) $/unit Hand-held calculators (1975-78) $/unit
0 .401 Disc memory drives (1 975-78) $/kilobit
I qj- PVC price (1 946-1 968) $/lb.
Steel production (1920-1 955) man-hrslton 0.30-
-~ i rc ra f t assembly (1 925-57) man-hrslunit Petroleum cracking (1942-58) $/bbl* Crushed limestone (1929-71 ) $/ton* MOS-LS1 production (1 970-76) $/unit
0.20- Petroleum refining (1 860-1962) man-hrslbbl
Model "T" Ford (1910-1 926) $/unit
0.10- Catalytic cracking (1946-1958) man-hrslbbl
Electric power generation (1910-1955) $/kwh"
0 I I 1 I I I 1
Slope of the Experience Curve
Source: Ayres, 1985 c.
Figure 1. Experience curve parameters for various industries.
- 13 -
For Kt > > 1 (9) reduces to
In this case it can be shown easily CAyres 85cI that the
condition for prow in^ profitability is
Condition (12) therefore requires v > 2 if b = 8.5 and a
> 10 if b = 0.1. The condition is relatively easily met for
fast gowing industries with large values of b (such as
semiconductors> but it cannot be sat isf led by more mature
industries with small values of b.
One obvious implication of the above result is that true
monopolists, who are fairly rare, -- in contrast to
Chamberlinian monopolists -- are likely to have less
incentive to adopt new production technologies than actively
competing firms. In practice, oligopolists in mature, slow-
growing industries (small b) do apparently have rather little
incentive to innovate. Among a number of competing firms,
however, the earlier adopter of a more efficient production
technology is the one who will gain a temporary advantage and
increase his prof itability, market share or both. (Here
long-term growth in profitability is not at issue). On the
other hand, if the innovation is unsuccessful, the early
adopter is worse off than the non-adopter. The choice, -- to
adopt, or not -- is then made on the basis of failure risk
, - ' vi= a vie perceived benefits in case of success [ Ayres & Mori
861. It is important to realize, however, that the "game" in
- 14 -
slow-growth industries is likely to be even less favorable
than "zero sum". In fact, if the innovation is a success
early adopters probably gain less than late adopters will
lose. The problem is that nobody can opt out of the game
(prisoners dilemma), so that change of any kind is risky.
The simple model above explicitly assumes that the
benefits to CIM adopters are reflected in lower costs, rather
than irLcreased demand due (for instance) to superior product
differentiability resulting in faster adaptation to market
changes.
However, the apparent limitation can be partially
overcome by adopting a Lancastrlarl point of view, namely that
product services are, in fact, differentiated bundles of
characteristics. A shift in demand function due to product
" improvement" is practically indistinguishable from a shift
in supply function due to process improvement. Either the
firm can provide more "utiles" per unit cost, or a given
number of "utiles" at less cost. The experience curve is
likely to be as applicable to the one case as to the other.
The analytical problem we must now face is as follows:
given a competitive market and a risky innovation of
uncertain success, how should a rational management play the
rame? And, given evidence of success by some early adopters, Y
how can "followers" be expected to react? These are s o m e ke-j
issues for future research.
'"'There is a considerable debate in the literature on the microeconomic foundations of -'experience curves' (e. g. Arrow, 1963, Alchian, 1963) but the empirical evidence is fairly convincing.
- 15 -
Profitability and Diffusionfl
The rate at which new technologies substitute for
established ones has often been found to follow an S curve
[ Fisher & Pry, 19711 . However, the underlying mechanisms for
this have never been fully explained. The most widely
accepted reason is that new technologies follow a first order
diffusion process (demand proportional to fractional market
penetration) and a second order saturation process. The
solution to the differential equation (df/dt = a£ - bf2:>
representing this situation, where f is the fractional market
penetration and a and b are constants, is the simplest form
of curve, known as a logistic function. While this model is
analytically simple and fits a wide variety of ex post data
[ibidl, it offers no clues for ex ante prediction of the rate
at which diffusion will occur. Much of the technological
forecasting literature has used this model assuming a prior1
that an S curve will represent the rate of introduction. The
usual procedure is to determine the parameters of the curve
by curve-fitting. An ex ante methodology is greatly to be
desired. Mansfield [Mansfield 61, 681 was the first to
attempt this task using econometric methods. More recent
efforts along these lines have been reported by Blackman
[Blackman 741, Martino [ Martino et al. 781 and others.
The rate at which initial diffusion occurs has been
found to depend empirically on the expected profitability of
the new technology, the absolute size of the investment, the
tendency for the industry to innovate, and the time-
"This section is based on a previously unpublished working paper by Jeffrey L . Funk and the author (dated January, 1983).
- 16 -
preference (or discount) factor. Profitablity can be
represented by a firm producing the product or using the new
technology at a rate that will maximize its present value
over a planning horizon. The size of the investment and the
industry will determine a firms's attitude towards risk and
short-term losses. The industry's tendency to innovate
should also affect the time horizon considered. These ideas
are the basis for the model described hereafter.
The rate at which a new technology is introduced in a
sector can be viewed as a summation of the rates at which
individual firms introduce the new technology. Each firm
will introduce the new technology in a way that will maximize
its objective function. We will assume the firm' s objective
is to maximize the present value of future prof its over some
time horizon, subject to a constraint on cumulative losses
allowed. The control variable for the problem is the price
P!t> or the quantity Q(t>, as a function of time. If the
price is set below cost the firm sells temporarily at a loss
but gains production experience permitting it to reduce its
costs. The maximization problem is represented
mathematically below:
Max W(t>
where
- 17 -
and
P(t) = unit price at time t
C(t> = unit cost at time t
Q(t> = quantity produced per unit time
6 = discount rate
Before considering more complex cases, it is interesting
to note that for the simple case of Chamberlinian monopolist
in a 'niche', confronting a fixed price elasticity w , and a
given market price, the optimal rate of CIM adoption k has
been shown (Ayres, 1985) to be as follows:
where 6 is the adopting firms effective discount rate, and r
is its target rate of return on investments. Alternatively
(r-6) represents the 'risk-premium' set by the firm, over and
above the discount rate.
A more complex model results if one introduces a loss
constraint. A constraint on the maximum loss per period can
be expressed as:
A total loss constraint could also be introduced. Firms
may have different cost functions, discount rates, cumulative
loss constraints, and demand curves. The cost function wiil
vary for each firm depending on its existing capital stock
and personnel but in general it will decline as a function of
~zumulative product ion experience [ e. g. Cunningham 881 . The
c o s t of e q u i t y and d e b t c a p i t a l a s w e l l a s management r i s k
p r e f e r e n c e s and p e r c e p t i o n s of f u t u r e p r o s p e c t s c a n r e s u l t i n
wide ly v a r y i n g d i s c o u n t r a tes CAyres & Mori 861. The
c u m u l a t i v e l o s s c o n s t r a i n t w i l l depend on a f i r m ' s l i q u i d i t y
and its management 's a t t i t u d e towards r i s k . The t i m e h o r i z o n
c o n s i d e r e d is a l s o a v a i l a b l e . I t p r o b a b l y depends on t h e
r a t e of exogenous t e c h n o l o g i c a l change, i . e . on t h e e x p e c t e d
t i m e b e f o r e t h e e x i s t i n g t e c h n o l o g y becomes o b s o l e t e . Other
d i f f e r e n c e s between f i r m s and t h e i r p r o d u c t s w i l l a f f e c t t h e
demand f o r a p roduc t a s a f u n c t i o n of p r i c e and o t h e r
a t t r i b u t e s . These d i f f e r e n c e s w i l l r e s u l t i n e a c h f i r m
i n t r o d u c i n g t h e new t e c h n o l o g y a t a d i f f e r e n t t i m e and r a t e .
New t e c h n o l o g i e s c a n be d i v i d e d i n t o new p r o c e s s e s which
produce o l d p r o d u c t s and new p r o d u c t s which a r e produced w i t h
e x i s t i n g o r new p r o c e s s e s . CIM is b a s i c a l l y a s e t of p r o c e s s
i n n o v a t i o n s . Old p r o d u c t s produced by a new p r o c e s s w i l l
no rmal ly be marketed i n i t i a l l y a t t h e same p r i c e a s t h e o l d
1 p r o c e s s t o p r e v e n t p r o d u c t s f rom t h e same f i r m f rom competing
w i t h e a c h o t h e r . Here t h e d e c i s i o n v a r i a b l e f o r t h e a d o p t e r 0 - *
is t h e q u a n t i t y of p r o d u c t s t o be produced by C I M v i s a v i s
t h e q u a n t i t y produced by t h e o l d p r o c e s s . Thus, f o r t h e
moment, w e c o n s i d e r o n l y t h e c a s e of a p roduc t demand curve
t h a t is n o t c h a n g i n g o v e r t i m e .
Cons ide r a (new) f i r m t h a t wishes t o adop t a new p r o c e s s
(:CIM> t o produce a n e s t a b l i s h e d p r o d u c t . The market p r i c e A
f o r t h e p r o d u c t is P. The CIM-adopter h a s u n i t c o s t s C that
w i l l d e c r e a s e a s a f u n c t i o n of c u m u l a t i v e o u t p u t by t h e new
p r o c e s s . I t is f r e e t o o f f e r its produc t a t a d i f f e r e n t
p r i c e P t h a t r n i ~ h t be e i t h e r h i g h e r o r lower t h a n 6. I t
confronts a constant demand function which is a function of A
both P and f, For the CIM adopter, the problem is expressed
by (13) above, where its cost function C is given by equation
(3) and N is given by equation ( 4 ) .
Let 6 be the quantity by the old process produced and
let f be the market penetration of the new process. It is
reasonable to assume that the market share of Q is a function A
of the relative prices P and P, but that -- for various
reasons (including inertia and 'intangibles') -- the market A
will tolerate some price differential (P Y P), even though
the products produced by CIM technology are assumed to be
identical to those produced by conventional technology.
However the market responds to any differential by increasing
demand for the lower priced source.
A mathematical relationship that satisfies this
condition (while being less restrictive than the constant
price elasticity assumption) is the following:
h
where Q is the quantity produced by conventional means
The parameters A , T and rr (see equation 1) are all to be
determined; P is a variable, while 6 is now assumed to be
constant.
- 28 -
Thus t h e CIM a d o p t e r now sees t h e problem a s :
where
and (15) must be s a t i s f i e d i n a l l p e r i o d s .
Taking t h e d e r i v a t i v e s w i t h r e s p e c t t o t h e t i m e t :
The mathemat ica l c o m p l e x i t y of t h i s f o r m u l a t i o n c o n c e a l s
a n e s s e n t i a l t r a d e o f f t h a t t h e CIM a d o p t e r must f a c e : I t s
c o s t s w i l l d e c r e a s e w i t h a c c u m u l a t i n g e x p e r i e n c e ; and its
c o s t s w i l l t h e r e f o r e f a l l f a s t e r i f it s e t s its i n i t i a l
( e n t r y ) p r i c e P a s low a s p o s s i b l e , t o g a i n t h e l a r g e s t
p o s s i b l e i n i t i a l market s h a r e . On t h e o t h e r hand, its
i n i t i a l u n i t c a s t s c a n be e x p e c t e d t o be h i g h , due t o break-
i n problems and it w i l l e x p e c t t o l o s e money f o r a whi le
T h e r e f o r e , t h e f a s t e r t h e i n t e n d e d p e n e t r a t i o n , t h e l a r g e r
t h e i n i t i a l l o s s . I t f o l l o w s t h a t ( i n t h i s model> t h e
p e n e t r a t i o n r a t e is l i m i t e d by t h e maximum a n n u a l s t a r t u p
l o s s t h a t can be s u s t a i n e d .
T h i s problem c a n be s o l v e d u s i n g Optimal C o n t r o l Theory
a s d e s c r i b e d i n t h e Appendix. When t h e r e isn't a n y
c o n s t r a i n t on t h e c u m u l a t i v e l o s s e s t h e d i f f u s i o n p r o c e s s
- 21 -
need not occur at a finite rate. Each curve is for a
different initial cost. Numerical solutions are shown in
Figure 2. The higher the initial cost the lower the final.
saturation level but the basic shape of the curve is not
changed. Cumulative revenues are shown in Figure 3 for the
same initial costs. Total profits (above an acceptable
return on equity) over twenty-five years decrease with higher
initial costs. If the initial cost was greater than C, = 23,
no production should occur because it would result in
negative profits. For lower initial costs the cumulative
revenues early in the life of the project are negative, which
requires liquid capital. The firm can go bankrupt if the
pool of liquid capital dries up before profitability is
achieved.
Because there is no penalty for decreasing output (thus
resulting in unused capacity), a cumulative loss constraint
causes the firm to have a discontinuous price path which
results in a discontinuous output path. In real life a firm
would not change its price instantaneously to eliminate
excess capacity or to achieve better customer relations in
the short run. This was resolved by assuming a constant
initial price (close to prices satisfying the necessary
conditions) until the costs were reduced to the initial price
without violating the cumulative loss constraint. The
solution then follows from the necessary conditions. This
produced continuous solutions for price and output. Market
penetration is shown in Figure 4 for price elasticities of . 5
and 1. There is some resemblance to a traditional S curve,
but the differences are significant.
I
I I I
5 10 15 20 25 Time
F i g u r e 3 . Cumula t ive revenues v s . t i m e For d i f f e r e n t i n i t i a l c o s t s .
- 25 -
Conclusion
In this paper, a simple dynamic model based on the
'experience curve' for estimating private benefits (to the
firm) is briefly discussed and some possible directions for
extension are indicated. An application of the model to
predicting penetration (or diffusion) rates is discussed
also.
It was pointed out that there is another dimension of
the problem, viz. to estimate social benefits. To be sure,
the likelihood of social benefits does not, in itself,
provide a motivation for private firms to adopt a new
technology. In a centrally planned socialist economy, of
course, such a distinction should (in principle) be
unnecessary. But quite apart from the motivational aspect,
there is a very important methodological problem to be faced.
As noted previously, we need a dynamic model for evaluating
social benefits of CIM (or other new technologies). Such a
model is suggested by Mori in the following paper and
preliminary results are obtained for the Japanese economy.
EEFEEEBCES
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CAyres-c 851 Ayres, Robert U.. A Schumpeterian Model of Technological Change, Journal of Technological Forecasting & Social Change 27(4>, 1985.
[Ayres-c 861 Ayres, Robert U.. Artificial Intelligence, Robotics & Integrated Manufacturing, Frometeus, 1986. [ NOTE: f orthcomingl
[ Ayres-f 861 Ayres, R. U. . Complexity, Re1 iabil ity And Design: The Coming Monolithic Revolution In Manufacturing, Working Paper (WP-86-48), I IASA, Laxenburg, Austria, August 1986.
[ Ayres-b 871 Ayres, R . U. . Future Trends In Factory Automation, Working Paper(W-87-22>, IIASA, Laxenburg, Austria, February 1987.
C AyreskFunk 851 Ayres, R. U. & Funk, J. L. . A Technological Forecast for CIM, Robotics and Computer-Integrated ~nufacturing, 1985. NOTE: f orthcomingl
[ Ayres&Hori 861 Ayres, R. U. & Mori, S. . Time Freference And The Life Cycle: The Logic Of Long-Term High Vs, Short-Term Low Risk Investment, Working Faper, I IASA, Laxenburg, Austria, October 1986. C NOTE: f orthcomingl
[ Blackman 741 Blackman, A. Wade. The Market Dynamics of Technological Substitutions, Technological Forecasting & Social Change 6, Feb 1974. : 4 1-63.
[ Eryson& 631 Bryson, A. e. , Jr. , Dengam, W. F. 8 Dreyfus, S. E. . Optimal Programming Problems with Inequality Constraint I: Necessary Conditions for Extremal Solutions, A/AA J. 1, 1963. : 2544-2550.
[Chamberlin 333 Chamberlin, E.H.. The Theory Of Monopolistic Competition: A Re-Orientation Of The Theory Of Value 38, Harvard Univ. Press, Cambridge, Fiss. , 1933. 7th edition.
[Charherlin 531 Chamberlin, E.H.. Product as an Economic Variable, Quarterly Journal of Economics 67 (3. I), 1953. : 1.
[ Cunningham 801 Cunningham, J . A. . Using the Learning Curve as a Management Tool, IEEE Spectrum, J un 1980.
[Fisher & Pry 711 Fisher, John C. & Pry, R. H.. A Simple Substitution Model of Technological Change, Technological Forecasting & Social Change 3(1), 1971.
[ Gulledge8EWomer 861 Gulledge, Thomas Jr. & Womer, Norman. The Economics Of hde-To-Order Production, Springer-Verlag, Berlin Heidelberg, New York, 1986.
[ HouthakkerhTaylor 701 Houthakker, H. S. & Taylor, L. D. . Consumer Demand In The United States: Analysis & Frojectlons, Harvard Univ. Press, 1970, I: NOTE: revised ed. I
[Mansf ield 611 Mansf ield, Edwin. Technical Change & the Rate of Imitation, Eoonometrica 29 (4), Oct 1961. : 741-766.
C Mansf ield 681 Mansf ield, Edwin. Industrial Research And Techno1 oglca1 Innovation, W. W. Norton, W , 1968.
[Martino& 781 Martino, J. P., Chen, K , , (L Lenz, R.C. Jr. . Predicting The Diffusion Rate Of Industrial Innovations, Final Report(UDR-TR-78-42>, University of Dayton Research Institute, Dayton, Ohio , March 1978.
C McCormick&Sanders 821 McCormick, Ernest h Sanders, Mark. Human Factors In Engineering And Design, McGraw-Hill Publ. Co., NY, 1982. 5th edition.
AFPEND I X
Introducing the Hamiltonian function:
where Q and p are adjoint variables for N and a respectiveiy, and
P, P, N, a, n and p are all functions of time. The optimal time
paths for N and P are determined by the necessary conditions of
Pantryagin' s maximum principle:
( 2 ) aH/'aP = 0
( 3 ) aH/aN = -drl/dt
(4) aH/an = - d ~ / d t
( 5 ) a ~ / a n = d ~ ~ / d t
(6) a~/a,, = dn/dt
( 7 ) 7 r > -D
( 8 ) rl (T) = 0
(9) p(T) = 0
From (I), ( 2 ) = 8 and using (9):
(10) p(it) = 8.
Applying the necessary conditions
Solving for P leaves two differential equations <13 and 14)
with two unknowns (N and n). When the cumulative loss constraint
is not violated a numerical solution can be found by assuming
r l < @ ) and solving difference equations iteratively until ,,(TI = 8
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1Ervso1~1 2;; al. (531. Thi:; w i l l . r e q u i r ? F ( ~ I = i I . kIi,en
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".rF;z -t - ,,-'. - - , ~ . e r - t h a n the! t:o.t,=.. iile rest , c.1 t h e ~ . o l . u t i ~ o r ~ ~ o l l o w : , fr-err:
L. - .rl - - - - ile e1.-- :=:=~fi~- .y g : o ~ - i c i i t i o r - ~ , % a<3 dc:sg:~-ibed ear lie^^.